Overview | Content Knowledge | Essential Questions | Connection To Standards | Initiating Activity | Learning Experiences | Culminating Performance | Pre-Requisite Skills | Modifications | Schedule/Time Plan | Technology Use
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LU Title: What's A Problem? |
Author(s): Kimberly Wells |
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Grade Level: 5 |
School : Sylvan-Verona Beach Elementary |
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Topic/Subject Area: Math |
Address: PO Box 246 Verona Beach, NY 13162 |
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Email: kwells@oneida-beach.moric.org |
Phone/Fax: 315-762-4404 |
This three week integrated unit incorporates
standards from MST and ELA. At the end of the unit, students will participate
in a problem solving activity with their parent or guardian. Students will use
skills learned throughout the unit while parents will use strategies that were
taught at a parent workshop to complete the culminating task. Students are
responsible not only to solve problems correctly; they are responsible to give
written explanations of their solutions.
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Declarative Students will: |
Procedural Students will: |
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Learn 7 problem solving strategies |
Utilize strategies to solve a variety of problems |
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Explain when a specific problem solving strategy would be used |
Create problems that are solved using a particular strategy |
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Understand why one strategy would be used instead of another |
Provide written explanations of problem solutions |
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Understand how these strategies can be used to solve real life problems |
Work cooperatively with peers and parents |
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Understand parts necessary to solve problems successfully |
Use a checklist for self evaluation |
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ESSENTIAL QUESTIONS
1.How can everyday materials be used
to solve real life problems?
2. Why is it
important to be able to solve the same problem a variety of ways?
3.Why is it important to have several ways to solve
problems?
CONNECTIONS TO NYS LEARNING STANDARDS
List
Standard # and Key Idea #: Write out related Performance Indicator(s) or
Benchmark(s)
MST
Standard 1 - Analysis, Inquiry, and Design
Students will use mathematical analysis, scientific inquiry, and
engineering design, as appropriate, to pose questions, seek answers, and
develop solutions.
Standard 2 -
Information Systems
Students will access,
generate, process, and transfer information using appropriate
technologies.
Standard 3 -
Mathematics
Students will understand
mathematics and become mathematically confident by communicating and reasoning
mathematically, by applying mathematics in real-world settings, and by solving
problems through the integrated study of number systems, geometry, algebra,
data analysis, probability, and
trigonometry.
ELA
Standard 1 Listening and Reading
Standard 1 Speaking and Writing
Students will be given a task to complete (see
initiating activity attachment). Put students on the clock and explain that
they have to solve problems and be able to explain how they solved them. The
teacher will ask the students to share their solution and the strategies they
used to solve the problems. After the discussion, chooses one or two problems
and show students the solutions using 2-3 different methods. Discuss the unit
that they are going to be studying, making sure to include the parent workshop
component.
LEARNING
EXPERIENCES
In chronological order including acquisition experiences and
extending/refining
experiences for all stated declarative and procedural
knowledge.
Strategies
Work Backwards, Use Objects, Draw a Picture, Make a Table, Make A List, Find a Pattern, Guess and Check
Declarative Knowledge
What declarative knowledge should students be in the process of acquiring and integrating? AS a result of this unit, the student will know or understand
What experiences or activities will be used to help students acquire and integrate knowledge?
What strategies will be used to help students construct meaning, organize, and/or store knowledge?
Procedural Knowledge
What procedural knowledge will students be in the process of acquiring and integrating? AS a result of the this unit, students will be able to:
What will be done to help students construct models, shape and internalize the knowledge?
Strategy #1
Guess and Check
Strategy #2
Work Backwards
Strategy #3
Find a Pattern
Strategy #4
Make a List
Strategy #5
Make a Table
Strategy #6
Draw a Picture
Strategy #7
Use Objects
Extending and Refining Activities
What knowledge will students be extending and refining?
What reasoning process will they be using?
Describe what will be done.
CULMINATING PERFORMANCE
Include rubric(s)
** EXTRA EXTRA **
PROBLEMS IN HONERIESWELL
The city of Honerieswell is faced with a terrible
dilemma. IN order for the great OHERWELLS to give away the treasured
foods of the city, they must find worthy candidates. You are on a mission to be
a worthy candidate. In the city, you are considered to be a world class problem
solver. In front of you are ten problems that the great OHERWELLS have
presented you with. After carefully reading all of them, chose the five that
you will solve to help solve the biggest problem, getting rid of the treasured
goods. The catch, you must use a different strategy to solve each one. In the
spaces below, write the problem number, the strategy you used and the process
you went through. You may use pictures, lists, or written explanations to show
how you solve them. Only citizens who use five of the seven problem solving
strategies will be considered to receive the treasured goods. Don't be alarmed,
there is enough treasure for all that accept this challenge and who
successfully complete it. Good Luck and thank you for your help in solving this
dilemma.
# of problem Strategy Solution
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Signature Required for Processing
____________________________
Notes from the GREAT
OHERWELLS
PROBLEMS
1. Kim has coins are worth $1.17, but she
can't make change for a dollar. What coins does she have?
2. Oh and Well are making final awards for the problem-solving contest. Each award has a blue and an orange ribbon on it. Each strip of ribbon is 23 cm long. How many meters will they need to make 35 awards?
3. When Chris was ten years old, he carved his girlfriend's name in the truck of the Elm Tree in his side yard, two feet above the ground. While Chris would only grow 1-2 inches a year, the tree would grow 6 inches. When Chris was 25, his new wife found the tree and saw what he had written. What height was the name on the tree?
4. Old McDonald had a farm, a wife, some horses and some geese. All together there were 24 animals living in his barn. How many geese and horses does Old McDonald have if there is a total of 62 feet seen under the stalls in the barn?
5. Complete the next 5 rows of this multiples triangle.
3 6 9
4 8 12 16
What is the last number in row 30?
6. Main Street Pizza was celebrating "Everyone Loves Pizza Week". They are selling one topping large pizzas for $5.00! You have decided that over the course of the week you are going to eat one of each type they make. They have 4 types of crusts plus their special thin n crispy. The toppings that are available are pineapple, pepperoni, mushroom, onion, anchovies, and sausage. How many different one topping pizzas will you have toe at this week?
7. Nichole wanted to know the age of the new Temur at the zoo. Jack, the zookeeper, told her that if she added ten years to the age of the Temur and the doubled it, the Temur would be 90 years old. How old is the Temur?
8. You are trying to balance a 14-pound bowling ball. Which of the following weights would you choose to balance the ball, 3 lb., 5 lb., 7 lb., 10 lb., 15 lb.? Hint: You will need to use more than one weight.
9. What two numbers form a sum of 475 and a difference of 177?
10. Find 3 numbers that when added or multiplied together, their sum and product are the same.
Problem Solving Task Evaluation Checklist
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#1 |
Student |
Parent |
Teacher |
Comments |
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Identifies strategy |
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Strategy fits problem |
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Uses strategy correctly |
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Explanation is clear |
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Parent Assistance |
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Neat & Organized |
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#2 |
Student |
Parent |
Teacher |
Comments |
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Identifies strategy |
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Strategy fits Problem |
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Uses strategy Correctly |
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Explanation is clear |
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Parent Assistance |
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Neat & Organized |
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#3 |
Student |
Parent |
Teacher |
Comments |
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Identifies strategy |
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Strategy fits |
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Uses strategy correctly |
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explanation is clear |
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Parent Assistance |
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Neat & Organized |
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#4 |
Student |
Parent |
Teacher |
Comments |
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Identifies Strategy |
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Strategy Fits problem |
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Uses strategy correctly |
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Explanation is Clear |
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Parent Assistance |
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Neat and Organized |
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#5 |
Students |
Parent |
Teacher |
Comments |
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Identifies Strategy |
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Strategy Fits Problem |
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Uses strategy correctly |
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Explanation is clear |
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Parent Assistance |
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Neat and Organized |
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PRE-REQUISITE SKILLS
Students need to know basic
computation.
Students may require additional assistance in using particular strategies. This may be done with the help of other students, the teacher or parents. For most students this is their first experience using specific problem solving strategies. Because of this, students will need time to experiment.
MODIFICATIONS
Because this unit is taught in small chunks,
students of all abilities will be able to complete the daily and culminating
assessments. The checklist will be used for all students but students will be
assessed on an individual basis, not compared to the rest of their peers.
This unit can be completed in 2 weeks when managed correctly. It is important however to be flexible if this is your student's first experience with this type of project. It is also important to plan more time then you feel will be necessary from your class if this is the first time you have tried this.
TECHNOLOGY USE
Students are required to complete a minimum of two problem solving experience during this unit. The may choose to use either the CD-ROM Mighty Math Number Heroes, where their work is kept directly in the computer or the may choose the web site activities Math Counts or Math For Kids (see attachments).
These are completed during the lessons. Students are able to use the
computers AFTER the guided practice part of the lesson. By waiting until this
part of the lesson, the teacher is able to o make sure that students understand
the concepts taught.
My suggestion would be to schedule
students on computers so that students who will have more difficulty with the
concepts will use the computer on a day where Make a List or Use an Object is
taught. These are two of the easier strategies and they have a better chance of
succeeding the first time with these, allowing them to use the computer.
Two of the computer activities are assessed directly on the
computer. One of the web sites has a teacher made handout that needs to be
turned in.
REFLECTION
One of the problems that I would like to address is that of parent participation. Our parents were motivated by our workshop and therefore were anxious to participate. However, I know this is not always the case. For students who do not have a parent or guardian to participate, I would encourage a teacher to work in that leadership role. I would make sure this is done after school or during a recess period though.
We also send a certificate to both the student and the parent upon completion of the problem solving assessment.
Attachments
Guess and Check
#1
Craig, Kim and BeeAnn spent Saturday afternoon Christmas shopping. Craig spent twice as much as money as Kim and $25 less than BeeAnn. If the total amount of money they spent was $95.00, how much did each spend?
#2
The LeBlanc family took a four-day vacation. They drove the same distance on Friday and Monday, but only 1/8 as far on Saturday and 1/6 as far on Sunday. Total mileage of the trip was 66o miles. How many miles did they drive each day?
#3
In preparing for their class trip, fifth graders at SVB held four fundraising activities. The bake sale netted $76 more than the book sale and $124 more than the dance. The school carnival netted $320 more than the bake sale. If the total amount raised was $916.00, how much did the students raise on each activity?
#4
First 8 is added to me, then I am multiplied by 3, then 30 is subtracted from me, and finally I am divided by 10. The result is 18. What number am I?
Work Backwards
#1
At a recent diving competition, Meg's scores for her first three dives were 9.1, 9.6 and 9.9. To win the competition, she needs an average score of 9.5. What score does she need on her fourth and last event in order to win the gold medal?
#2
Kim gave a problem to Chris. She told him to pick a number, add 8 to it, triple that sum and then subtract 26. His answer was 67. What number did he pick?
#3
All of the houses on Uncle Sam's Drive are red, white or blue. There are twice as many white houses as red houses. There are 5 more red houses than blue houses. There are 7 blue houses. How many houses are there on Uncle Sam's Drive?
#4
The Oneida Basketball Team scores 100 or more points a game. In todays games, Justin, Sam, Mark, and Michael do all of the scoring for the team. Sam scores 10 more points than Justin. Mark scores 9 fewer points than Sam. Michael scores twice as many points as Mark. At the end of the game, the highest scorer is Michael, with 42 points. How many points did the Oneida Basketball Team make?
#5
Hope, Kaylee, Morgan and Patrick are running for class president. Hope receives 40 more votes than Kaylee. Kaylee receives two-thirds as many votes as Morgan, and Morgan receives one-half as many votes as Patrick. Patrick receives exactly 60 votes. Who wins the election?
Find a Pattern
#2
The Clock is Ticking- After two minutes of a basketball game, The SVB Lakers were leading 8 to 3. If this pattern continued, what would the score be after 10 minutes?
#3
At the end of the game, the scorekeeper noticed an unusual pattern in the SVB Lakers scoring. The scores in the book showed that Player 1 scored 1 point. Player 3 scored 4 points. Player 5 scored 9 points. How many points did player number 9 score? How many did number 11 score?
#4
In a game, Chris took several different kinds of shots. First he would try a 2-point shot and then he would follow it with a three-point shot. How many points would Chris have scored if he attempted 20 shot and made every third try?
Make a List
#2
Soda Anyone?-Jolene puts 65 cents into the soda machine. The machine takes quarters, dimes and nickels. To buy a soda, Jolene must use exact change. What coins could she use to buy a soda?
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Checkerboard Fun-Using a checkerboard, determine how many squares of all sizes are on a checkerboard.
#4
Chris won trophies for his achievement in baseball, football and basketball. How many different ways can he arrange these in his trophy case?
#5
Craig won a certificate for a free ice cream cone at the school fair. The cone is for a dynamite double scoop cone. He has 8 flavors that he can choose from. He refuses to get 2 scoops of the same flavor and he will not eat cookies and cream with orange sherbet. How many choices does Craig have for his cone?
Make a Table
#1 Award Winning Musicians-
Three children are each preparing to play their instrument in an upcoming concert. One child is a drum player. From the clues below, find the name of the child, their ages and what kind of instrument they are playing.
Clues:
The child playing the drums is younger than
BeeAnn.
Kim is the oldest.
The clarinet player is a girl.
The kids are 10, 11 and 12.
The instruments are the flute, clarinet and the
drums.
#2- Collectors- Three children are each preparing a collection as part of a hobby show. One child collects Pokemon cards. Using the clues below, can you find the names of the children, their ages and what they collect?
Sam is the oldest.
The Pokemon collector is a girl.
The child who collects Beanie Babies is younger than
Chris.
The Children's names are Sam, Chris, and Abby.
They are 8. 9. And 10 years old.
They collect Beanie Babies, Pokemon Cards and
Pogs.
#3
Camera- If a camera takes 64 pictures every second, how many pictures does this camera take in ten minutes?
#4
Who is married to whom?-Chris, Craig, Tom and Steve are married to Kim, Lori, Bee and Melissa, although not necessarily in that order. Lori, who is Craig's sister, has four children. Chris and his wife have no children. Chris has never introduced his wife to Bee, who works late hours for Craig (but is not his wife; and Kim is considering telling Craig's wife to watch out). Craig and Tom are twin brothers. Who is married to whom?
#5
Sue wants to make a play area for her children outside her home. She has 30 meters of fence that can be used to make the children's play area. How should Sue build the play space so that is has the biggest possible area? (Think area and perimeter) What are the dimensions of the biggest area? What shape is it?
Draw A Picture
#1
At the Sectional basketball game, there were two empty seats from every three seat that wee occupied. If there are 35 seats in the section, how many are empty? How many are full?
#2
The cheerleaders want to build a 4-layer pyramid for half time of the homecoming football game. They want to have 4 people on the bottom and one on the top. How many cheerleaders are needed to build the pyramid?
#3
The cheerleaders want to build a 7-layer pyramid for half time of the homecoming football game. They want to have 7 people on the bottom and one on the top. How many cheerleaders are needed to build the pyramid?
#4
On her bicycle trip, Sis started in Ozwald and rode through four other towns along County Route 1. Phido is twice as far from Ozwald as Joker was; Phido was also the same distance from Joker as it was from Sylvan Lake. Steamy River was only 3 miles beyond Phido. Name the towns Sis rode through in order.
#5
Shelly's mom wanted to do something special for her birthday. She decided she wanted to make her a soccer cake. Shelly's mom is not the best baker though, so she decided to make just a plain round cake, frost it white and then put soccer ball candies and flags around the edges. She placed the flags around the cake and between each, she but a candy ball. She put 14 balls on the cake. How many flags were there?
Use Objects
#4
Jason has a three-liter unmarked container, a five-liter unmarked container and an unlimited supply of Mountain Dew. He decided to share a little of his rootbeer with his friend Sal, but only 4 liters. How can he give Sal only four liters?
#5
Using a balance scale, you must be able to balance every whole kilogram amount from 1 kg through 15 kg. You may choose four standard weights to use, each a different number of kilograms. What weights will you use?
Problem Solving Strategies
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Strategy |
1-5 Difficulty |
1-5 Usage |
Pros |
Cons |
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Guess and check |
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Make a List |
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Work Backward |
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Use Objects |
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Look for a Pattern |
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Draw A Picture |
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Make A Table |
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Name _______________________ Date _____________________
Math For Kids
1.Log into the computer.
2.Type in http://prince.thinkquest.org/4471/
3.Choose Take the Challenge-try our word problems.
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Step 2- Step 3- Step 4- |
6.Step 1 Step 2- Step 3- Step 4- |
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2.Step 1 Step 2- Step 3- Step 4- |
7.Step 1 Step 2- Step 3- Step 4- |
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3.Step 1 Step 2- Step 3- Step 4- |
8.Step 1 Step 2- Step 3- Step 4- |
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4.Step 1 Step 2- Step 3- Step 4- |
9.Step 1 Step 2- Step 3- Step 4- |
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5.Step 1 Step 2- Step 3- Step 4- |
10.Step 1 Step 2- Step 3- Step 4- |
NUMBER CORRECT ______ NUMBER ATTEMPTED 40
Name _____________________ DATE__________________________
Math Counts